{"id":"https://openalex.org/W1958607180","doi":"https://doi.org/10.1007/s10898-015-0343-y","title":"Eigenvalue analysis of constrained minimization problem for homogeneous polynomial","display_name":"Eigenvalue analysis of constrained minimization problem for homogeneous polynomial","publication_year":2015,"publication_date":"2015-08-13","ids":{"openalex":"https://openalex.org/W1958607180","doi":"https://doi.org/10.1007/s10898-015-0343-y","mag":"1958607180"},"language":"en","primary_location":{"id":"doi:10.1007/s10898-015-0343-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10898-015-0343-y","pdf_url":null,"source":{"id":"https://openalex.org/S115925768","display_name":"Journal of Global Optimization","issn_l":"0925-5001","issn":["0925-5001","1573-2916"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Global Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1302.6085","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100653856","display_name":"Yisheng Song","orcid":"https://orcid.org/0000-0002-9298-8778"},"institutions":[{"id":"https://openalex.org/I14243506","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98","country_code":"HK","type":"education","lineage":["https://openalex.org/I14243506"]},{"id":"https://openalex.org/I75955062","display_name":"Henan Normal University","ror":"https://ror.org/00s13br28","country_code":"CN","type":"education","lineage":["https://openalex.org/I75955062"]}],"countries":["CN","HK"],"is_corresponding":true,"raw_author_name":"Yisheng Song","raw_affiliation_strings":["Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong","School of Mathematics and Information Science, Henan Normal University, XinXiang, 453007, Henan, People\u2019s Republic of China","School of Mathematics and Information Science, Henan Normal University, XinXiang, 453007, Henan, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong","institution_ids":["https://openalex.org/I14243506"]},{"raw_affiliation_string":"School of Mathematics and Information Science, Henan Normal University, XinXiang, 453007, Henan, People\u2019s Republic of China","institution_ids":["https://openalex.org/I75955062"]},{"raw_affiliation_string":"School of Mathematics and Information Science, Henan Normal University, XinXiang, 453007, Henan, People's Republic of China","institution_ids":["https://openalex.org/I75955062"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5011886900","display_name":"Liqun Qi","orcid":"https://orcid.org/0000-0002-1112-5250"},"institutions":[{"id":"https://openalex.org/I14243506","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98","country_code":"HK","type":"education","lineage":["https://openalex.org/I14243506"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Liqun Qi","raw_affiliation_strings":["Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong","institution_ids":["https://openalex.org/I14243506"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100653856"],"corresponding_institution_ids":["https://openalex.org/I14243506","https://openalex.org/I75955062"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2780},"apc_paid":null,"fwci":2.948,"has_fulltext":false,"cited_by_count":56,"citation_normalized_percentile":{"value":0.91198502,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"64","issue":"3","first_page":"563","last_page":"575"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.974399983882904,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9704999923706055,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.8952121734619141},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6966387033462524},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.6622100472450256},{"id":"https://openalex.org/keywords/pareto-principle","display_name":"Pareto principle","score":0.6139777302742004},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.6101821660995483},{"id":"https://openalex.org/keywords/divide-and-conquer-eigenvalue-algorithm","display_name":"Divide-and-conquer eigenvalue algorithm","score":0.5171177387237549},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4852595031261444},{"id":"https://openalex.org/keywords/homogeneous","display_name":"Homogeneous","score":0.46482279896736145},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4585414528846741},{"id":"https://openalex.org/keywords/homogeneous-polynomial","display_name":"Homogeneous polynomial","score":0.4561757743358612},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.42507821321487427},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.32466915249824524},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.277121901512146},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.20002031326293945},{"id":"https://openalex.org/keywords/matrix-polynomial","display_name":"Matrix polynomial","score":0.19844871759414673},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09335753321647644},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.04748311638832092}],"concepts":[{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.8952121734619141},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6966387033462524},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.6622100472450256},{"id":"https://openalex.org/C137635306","wikidata":"https://www.wikidata.org/wiki/Q182667","display_name":"Pareto principle","level":2,"score":0.6139777302742004},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.6101821660995483},{"id":"https://openalex.org/C192702615","wikidata":"https://www.wikidata.org/wiki/Q5283998","display_name":"Divide-and-conquer eigenvalue algorithm","level":3,"score":0.5171177387237549},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4852595031261444},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.46482279896736145},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4585414528846741},{"id":"https://openalex.org/C17103678","wikidata":"https://www.wikidata.org/wiki/Q1474074","display_name":"Homogeneous polynomial","level":4,"score":0.4561757743358612},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.42507821321487427},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32466915249824524},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.277121901512146},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.20002031326293945},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.19844871759414673},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09335753321647644},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.04748311638832092}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1007/s10898-015-0343-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10898-015-0343-y","pdf_url":null,"source":{"id":"https://openalex.org/S115925768","display_name":"Journal of Global Optimization","issn_l":"0925-5001","issn":["0925-5001","1573-2916"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Global Optimization","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1302.6085","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1302.6085","pdf_url":"https://arxiv.org/pdf/1302.6085","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.745.8446","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.745.8446","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1302.6085.pdf","raw_type":"text"},{"id":"pmh:oai:RePEc:spr:jglopt:v:64:y:2016:i:3:d:10.1007_s10898-015-0343-y","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10898-015-0343-y","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"},{"id":"pmh:oai:RePEc:spr:jglopt:v:64:y:2016:i:3:p:563-575","is_oa":false,"landing_page_url":"http://hdl.handle.net/10.1007/s10898-015-0343-y","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:ira.lib.polyu.edu.hk:10397/19010","is_oa":false,"landing_page_url":"http://hdl.handle.net/10397/19010","pdf_url":null,"source":{"id":"https://openalex.org/S4306400205","display_name":"PolyU Institutional Research Archive (Hong Kong Polytechnic University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I14243506","host_organization_name":"Hong Kong Polytechnic University","host_organization_lineage":["https://openalex.org/I14243506"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal/Magazine Article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1302.6085","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1302.6085","pdf_url":"https://arxiv.org/pdf/1302.6085","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W1543439990","https://openalex.org/W1555881074","https://openalex.org/W1602295990","https://openalex.org/W1656443807","https://openalex.org/W1970563156","https://openalex.org/W1971702983","https://openalex.org/W1973940690","https://openalex.org/W2020374088","https://openalex.org/W2026856626","https://openalex.org/W2029590768","https://openalex.org/W2037934905","https://openalex.org/W2041197939","https://openalex.org/W2046253489","https://openalex.org/W2048024795","https://openalex.org/W2055869091","https://openalex.org/W2065243655","https://openalex.org/W2086589508","https://openalex.org/W2090208105","https://openalex.org/W2095180325","https://openalex.org/W2110174793","https://openalex.org/W2113722075","https://openalex.org/W2123825790","https://openalex.org/W2133651354","https://openalex.org/W2147475415","https://openalex.org/W2150544307","https://openalex.org/W2151293435","https://openalex.org/W2159552694","https://openalex.org/W2952501628","https://openalex.org/W2963659248","https://openalex.org/W2964080567","https://openalex.org/W3102798416","https://openalex.org/W3149666478","https://openalex.org/W3199893329","https://openalex.org/W4301791716"],"related_works":["https://openalex.org/W2477876258","https://openalex.org/W2099222495","https://openalex.org/W4385571797","https://openalex.org/W3151522584","https://openalex.org/W1511852063","https://openalex.org/W1497123311","https://openalex.org/W4378499136","https://openalex.org/W2163224973","https://openalex.org/W2358814668","https://openalex.org/W1958607180"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":8}],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2025-10-10T00:00:00"}